A response function describes a relationship between inputs and outputs of a device. For example, a radiometric response function of an optical device, such as a camera, relates irradiance received by the optical device to a brightness of an image obtained thereby. Given a set of input data and corresponding output data of a device, a response function thereof may be determined by finding a function that will fit or best fit the given set of the input and output data. Based on the determined response function, the inputs of the device may be reconstructed from respective outputs. For example, information of distribution of light intensities entering a camera may be reconstructed from pixel intensities of an image based on a determined response function of the camera.
Information of this set of input and output data, however, may not always be available for every device in every scenario. For example, amounts of sensor irradiance to a camera are normally unavailable in most scenarios. Nevertheless, a radiometric response function of a camera is normally made to be nonlinear for purposes such as compressing a dynamic range of sensor irradiance and/or adapting to a non-linear mapping of a display. This nonlinearity, if not accounted for however, may create problems in computer vision applications, especially when a linear relationship between sensor irradiance and recorded intensity of the camera is erroneously assumed. Therefore, radiometric calibration has become important for those computer vision applications that assume a linear relationship between sensor irradiance and recorded intensity.
Although a variety of algorithms have been proposed for determining a response function, for example, calibrating a radiometric response function of a camera, these algorithms are ad hoc in nature and fail to provide a unified framework for determining the response function.